Existing research on export heterogeneity between countries has typically focused on the importance of individual factors. This column presents a unified framework for understanding these contributions in concert. Using US and Chilean data, it demonstrates that products within firms, firms within sectors, and sectors in aggregate are indeed imperfect substitutes. It further shows that models that assume no quality shifts and no changes in variety perform poorly on trade data.

Economists have hypothesised many reasons why some countries export more than others. The most prominent explanations for understanding export behaviour focus on differences in prices, quality, firm heterogeneity (e.g. superstar exporters), and the entry and exit of firms and products (‘entry/exit’). While prior work has examined the importance of each of these forces, we have lacked a unified framework for understanding the contributions from each force towards countries’ overall patterns of comparative advantage. For example, the remarkable increase in Chinese export growth has been the subject of a large and growing literature including, for example, Autor et al. (2013) and Amiti et al. (2017), but a comprehensive evaluation of the sources of this export growth has remained elusive. In a recent paper, we show that this export growth can be exactly decomposed into the four main forces highlighted in existing trade theories (Redding and Weinstein 2017).

Most existing theoretical research has focused on relative prices across countries and sectors as the key drivers of comparative advantage. However, if products and firms within sectors are imperfect substitutes, the evolution of trade flows across countries and sectors also depends on changes in the average quality of goods, the variety of these goods, and the dispersion of quality-adjusted prices across these goods (the importance of superstar firms or goods). We find that these non-conventional forces dominate the conventional considerations of price in accounting for observed patterns of international trade. For example, increases in average quality and variety together account for all of the growth in China’s exports over our sample period, with rising Chinese relative prices actually reducing Chinese exports by around 17%, consistent with a story in which Chinese exporters gained market share by increasing both quality and price. Similarly, a geometric average of import prices is an important component of our theory-based aggregate import price index, and closely matches the growth in the official US import price index. However, this component substantially overstates the overall increase in our theory-based import price index by close to 2% per year, largely because of the proliferation of variety and improvements in quality over time.

Our work differs from existing research on trade patterns and the effect of trade on domestic prices, which has typically followed one of two approaches. On the one hand, general equilibrium ‘macro’ models of trade explain aggregate trade patterns based on assumptions about disaggregated economic activity. On the other hand, ‘micro’ studies of firm export and import behaviour use disaggregated datasets on firm-level trade decisions. While each line of research has informed the other, a substantial gap remains between the two approaches. The reduced-form nature of the micro studies means that there is no clear mapping between what happens at the firm level and what happens at the aggregate level. Similarly, the supply-side assumptions of the macro models can be at odds with what researchers observe in the micro data. In contrast, we develop a framework for aggregating from micro trade transactions by firm, product, source, and destination to macro trade and prices. Our framework is thus the first to exactly rationalise observed trade flows at both the aggregate and disaggregate level, which enables us to quantify the relative importance of different micro mechanisms for macro trade and prices. We thus inform recent empirical research on the margins of international trade such as Feenstra (1994) and Hummels and Klenow (2005), providing a framework that directly connects theory and data

We use our framework to derive price indices that summarise the cost of sourcing goods from each country and sector. We develop a theory-consistent measure of revealed comparative advantage, which depends on the relative values of these price indices across countries and sectors. We show that these relative price indices are weakly related to standard empirical measures of average prices, thereby providing insight for elasticity puzzles, in which real variables respond weakly to these empirical proxies. We use our model to decompose these price indices and comparative advantage into the contributions of a number of different micro mechanisms in a sequence of steps. First, we show that relative price indices depend on contributions from entry/exit and demand-adjusted prices. Second, we break out the demand-adjusted price term into contributions from the average and dispersion of demand-adjusted prices. Third, we separate out the average demand-adjusted price term into contributions from average demand and average prices. In the special case in which goods are perfect substitutes, only average demand-adjusted prices matter, because all varieties consumed have the same demand-adjusted price, and the consumer is indifferent between all these consumed varieties. More generally, if goods are imperfect substitutes, these price indices are decreasing in the number of varieties, because of consumer love of variety. Similarly, in this more general case, greater dispersion of demand-adjusted prices across varieties reduces these price indices, because it implies that consumers can more easily substitute from less to more attractive varieties.

We implement our approach using US import data from 1997-2011 and present a robustness test using Chilean data from 2007-14. We demonstrate the same qualitative and quantitative pattern of results in these two different contexts. In both cases, we estimate that products within firms, firms within sectors, and sectors in aggregate demand are indeed imperfect substitutes. For the US, we estimate a median elasticity of substitution across products of 6.3, a median elasticity across firms of 2.7, and an elasticity across sectors of 1.4. We show that these findings of imperfect substitutability have important implications for patterns of comparative advantage. Firm entry/exit and the dispersion of quality-adjusted prices each account for around one third of the cross-section variation in patterns of trade across countries and sectors. By contrast, average quality and average prices contribute just over 20% and just under 10%, respectively, to the total variation. For changes in trade patterns over time, the results are even more stark. Firm entry/exit and average quality each account for around 45% of the variation, with the dispersion of demand-adjusted prices making up most of the rest. We demonstrate that this pattern is robust across a range of alternative values for the elasticities of substitution. Indeed, for parameter values for which goods are imperfect substitutes, we show that the contributions from firm entry/exit and the dispersion of quality-adjusted prices to patterns of trade are invariant to these assumed elasticities.

As our framework exactly rationalises the observed trade data at both the disaggregate and aggregate levels, there is an exact mapping between our relative price indices and observed patterns of trade. However, the same need not be true for other approaches that impose stronger assumptions, such as the Feenstra (1994) price index, which corresponds to a special case of our framework that assumes no quality shifts for products sold in any pair of periods. Comparing our framework to these special cases, we find that models that assume no quality shifts and no changes in variety perform poorly on trade data. Models that incorporate variety changes while maintaining the assumption of no quality shifts do better, but can still only account for a relatively small proportion of changes in comparative advantage over time. These findings highlight the importance of changes in quality within surviving varieties in understanding the changes in comparative advantage documented in Freund and Pierola (2015) and Hanson et al. (2015). They also point to the relevance of dynamic trade theories, in which comparative advantage evolves endogenously with process and product innovation, as in Grossman and Helpman (1991).

Finally, as our approach uses only demand-side assumptions, we are able to provide empirical evidence on the supply-side distributional assumptions that are made in existing research. We find that standard supply-side distributional assumptions such as Pareto or log-normal productivity distributions are rejected by the data. However, we show that if one rationalises the data using our price index, distributional assumptions about the underlying parameters do not matter, as long as the distributions are centred on the correct mean of the logs of prices, demand/quality, and expenditure shares. As these means and the elasticities of substitution between firms and products are sufficient statistics for the costs of sourcing goods from each exporter and sector, they are all that matters for patterns of comparative advantage across countries and sectors, and the aggregate cost of living.